 Hello and welcome to the session. I am Deepika and I am going to help you to solve the following question. The question says solve for x and y, x plus 1 over 2 plus y minus 1 over 3 is equal to 8, x minus 1 over 3 plus y plus 1 over 2 is equal to 9. Now we can solve these equations by any algebraic method that is either by substitution method or by elimination method or by cross multiplication method. So let us solve these equations by elimination method. So let's start the solution. Now the given pair of linear equations is x plus 1 over 2 plus y minus 1 over 3 is equal to 8. Let us give this as number 1 and x minus 1 over 3 plus y plus 1 over 2 is equal to 9. Let us give this as number 2. Now the above equations can be rewritten as 2x plus 1 plus 2 into y minus 1 is equal to 6 into a and 2 into x minus 1 plus 3 into y plus 1 is equal to 6 into 9. Or these can be written as 3x plus 3 plus 2y minus 2 is equal to 48 and 2x minus 2 plus 3y plus 3 is equal to 54. Or these can be written as 3x plus 2y is equal to 48 minus 1 which is equal to 47 and 2x plus 3y is equal to 54 minus 1 which is equal to 53. Now let us give this as number 3 and this equation as number 4. Now we will multiply equation 3 by 2 and equation 4 by 3 to make the coefficients of x equal. So on multiplying equation 3 by 2 and equation 4 by 3 we get 6x plus 4y is equal to 94 and 6x plus 9y is equal to 159. Now let us give this equation as number 5 and this equation as number 6. Now we will subtract equation 6 from equation 5 to eliminate x because the coefficients of x are same. So on subtracting we get minus 55 is equal to minus 65 or y is equal to 65 upon 5 which is equal to 13. Now we will substitute this value of 5 in equation 3. Now equation 3 is 3x plus 2y is equal to 47. So on substituting the value of y in equation 3 we get 3x plus 2 into 13 is equal to 47 or 3x plus 26 is equal to 47 or 3x is equal to 47 minus 26 or 3x is equal to 21 or x is equal to 21 upon 3 which is equal to 7. Hence x is equal to 7 and y is equal to 13 is the required solution. So this is the answer of the above question. This completes our session. I hope the solution is clear to you. Bye and have a nice day.